The feeding and fasting cycles are strong behavioral signals that entrain biological rhythms of the periphery. The feeding rhythms synchronize the activities of the metabolic organs, such as liver, synergistically with the light/dark cycle primarily entraining the suprachiasmatic nucleus. The likely phase misalignment between the feeding rhythms and the light/dark cycles appears to induce circadian disruptions leading to multiple physiological abnormalities motivating the need to investigate the mechanisms behind joint light-feeding circadian entrainment of peripheral tissues. To address this question, we propose a semimechanistic mathematical model describing the circadian dynamics of peripheral clock genes in human hepatocyte under the control of metabolic and light rhythmic signals. The model takes the synergistically acting light/dark cycles and feeding rhythms as inputs and incorporates the activity of sirtuin 1, a cellular energy sensor and a metabolic enzyme activated by nicotinamide adenine dinucleotide. The clock gene dynamics was simulated under various light-feeding phase relations and intensities, to explore the feeding entrainment mechanism as well as the convolution of light and feeding signals in the periphery. Our model predicts that the peripheral clock genes in hepatocyte can be completely entrained to the feeding rhythms, independent of the light/dark cycle. Furthermore, it predicts that light-feeding phase relationship is a critical factor in robust circadian oscillations.